The present invention relates to a magnetic resonance (MR) imaging apparatus for imaging the interior of an object to be inspected by utilizing a MR phenomenon and more particularly, to a technique of obtaining blood flow velocity images.
The following literatures (1) to (3) disclose prior arts for obtaining blood flow images:
1) G. L. Dumoulin, S. P. Souza, M. F. Walker, and W. Wagle, "Three-Dimensional Phase Contrast Angiography", Magnetic Resonance in Medicine, Vol. 9, pp. 139-149 (1989). (hereinafter referred to as prior art (1)) PA1 (2) Y. Machida, N. Ichinose, H. Sugimoto, T. Goro, and J. Hatta, "Dual Velocity Sensitive Tetrahedral Flow Encoding MR Angiography", Proceedings of Society of Magnetic Resonance in Medicine, Eleventh Annual Scientific Meeting, p. 2810 (1992). (hereinafter referred to as prior art (2)) PA1 (3) M. F. Walker, S. P. Souza, and C. L. Dumoulin, "Quantitative Flow Measurement in Phase Contrast MR Angigraphy", Journal of Computer Assisted Tomography Vol. 12, no. 2, pp. 304-313 (1988). (hereinafter referred to as prior art (3)) PA1 x-direction flow velocity image EQU Vx=a*(.phi.(G.sub.1, G.sub.3)+.phi.(G.sub.2, G.sub.4))/4 PA1 y-direction flow velocity image EQU Vy=a*(.phi.(G.sub.1, G.sub.2)+.phi.(G.sub.3, G.sub.4))/4 PA1 z-d-rection flow velocity image EQU Vz=a*(.phi.(G.sub.1, G.sub.3)-.phi.(G.sub.2, G.sub.4))/4 PA1 absolute value image of flow velocity EQU V=.sqroot. (Vx*Vx+Vy*Vy+Vz*Vz) PA1 Further, flow velocity images may be calculated as follows: PA1 x-direction flow velocity image EQU Vx=a*(.phi.(G.sub.1, G.sub.3)+.phi.(G.sub.2, G.sub.4))+.phi.(G.sub.1, G.sub.4)+.phi.(G.sub.2, G.sub.3))/8 PA1 y-direction flow velocity image EQU Vy=a*(.phi.(G.sub.1, G.sub.2)+.phi.(G.sub.3, G.sub.4))+.phi.(G.sub.1, G.sub.4)-.phi.(G.sub.2, G.sub.3))/8 PA1 z-direction flow velocity image EQU Vz=a*(.phi.(G.sub.1, G.sub.3)-.phi.(G.sub.2, G.sub.4))+.phi.(G.sub.1, G.sub.2)-.phi.(G.sub.3, G.sub.4))/8 PA1 absolute value image of flow velocity EQU V=.sqroot. (Vx*Vx+Vy*Vy+Vz*Vz) PA1 x-direction flow velocity image EQU Vx=a*.phi.(G.sub.1 +G.sub.2, G.sub.3 +G.sub.4)/2 PA1 y-direction flow velocity image EQU Vy=a*.phi.(G.sub.1 +G.sub.3, G.sub.2 +G.sub.4)/2 PA1 z-direction flow velocity image EQU Vz=a*.phi.(G.sub.1 +G.sub.4, G.sub.2 +G.sub.3)/2 PA1 absolute value image of flow velocity EQU V=.sqroot. (Vx*Vx+Vy*Vy+Vz*Vz)
The prior art (1) describes 6-component chase contrast pulse sequences in which a set of flow encode pulses of different polarities are used in three-axis directions and signals corresponding to three-dimensional flow velocities in the three directions are acquired through a total of 6 kinds of measurement operations or cycles.
On the basis of the thus obtained 6 kinds of measured signals, a difference between paired measured signals is calculated to produce three kinds of signals including flow velocity information pieces in the three directions (x, y, z). The thus produced signals are reconstructed by a two-dimensional Fourier transform method to form three kinds of three-dimensional image data pieces reflecting flow velocities in the respective directions. On the basis of the thus formed three kinds of three-dimensional image data pieces, three-dimensional angiographic data which is blood vessel (blood flow) imaging data which reflects the magnitude of flow velocities.
The three-dimensional angiographic data is used for observation of images of individual slices or is subjected to the projection processing and used for formation of projecting images. There are various kinds of projecting methods and integrated projection and maximum pixel projection are described. Maximum intensity projection (MIP) is described as being available as the maximum pixel projection.
In FIG. 2 of prior art (1), only three kinds of signal data pieces having flow velocity sensitivity are described but practically, signal data having flow velocity sensitivity in one direction is produced as a difference signal between signal data obtained by applying a "+" flow encode pulse in the one direction and signal data obtained by applying a "-" flow encode pulse in the one direction.
Accordingly, from the standpoint of the manner of applying the flow encode pulse in prior art (1), two signal measurement cycles are carried out to obtain flow velocity sensitive signal data on one axis and six signal measurement cycles in total are effected on three axes and therefore, this method is called 6-component phase contrast pulse sequences.
The methods for performing imaging with phase sensitivity of 6 components and 4 components are generally called phase contrast pulse sequences.
Prior art (2) describes a measuring method of tetrahedral measuring type which is a kind of 4-component phase contrast pulse sequences in which measurement is carried out using four kinds of flow encode pulse patterns, measured data pieces are reconstructed and thereafter values approximately proportional to flow velocities are calculated.
Prior art (2) shows that even with the 4-component phase contract pulse sequences of tetrahedral type, three-dimensional angiographic data reflecting the magnitude of flow velocities can be obtained. This prior art method is similar to the 6-component sequences of prior art (1).
Prior art (3) describes a method in which a plurality of measured data pieces with different flow encode pulse patterns are reconstructed and flow velocities are determined by using phase information of the reconstructed images. Since the flow velocities are determined by evaluating the phases of the measured data pieces, accurate determination of flow velocities can be ensured in the case of a flow which is at a constant velocity and has no flow velocity distribution in a cross section.
Even in the presence of a flow velocity distribution in a cross section, a detailed analysis has been made to introduce a correction formula for determining an average flow velocity. For non-steady flow which is not at a constant velocity, an analysis has also been made.
In prior art (1), a complex difference between data obtained when the flow encode is positive and data obtained when the flow encode is negative is calculated to form three-dimensional angiographic data and data value depends on not only the flow velocity but also the excited state of magnetization, indicating that the data is not obtained by quantitatively determining flow velocities. In prior art (2), angiographic data depending on flow velocities can be obtained as in the case of prior art (1) but the flow velocities cannot be determined quantitatively.
In prior art (3), the flow velocity is determined by evaluating the phase. But the phase is evaluated in connection with each measured data pieces and consequently, the aliasing error is increased. The aliasing error raises the following problem when the phase exceeds the phase evaluation range of from -.pi. radians to .pi. radians. More particularly, since a measured value takes a value which is caused to fall in the range of from -.pi. radians to .pi. radians by being added with or subtracted by integer times the 2.pi. radians, a large measurement error takes place.
Especially, when offset of the phase is added because of non-uniformity of the static magnetic field, aliasing is caused by a slight change in phase due to flow velocity. Accordingly, the processing of removing offset due to the non-uniformity of static field is required.
When measurement of prior art (2) is carried out, calculation is effected as shown in FIG. 3 by the method of prior art (3) for independently evaluating the phases of individual measured data pieces.
FIG. 3 shows calculation effected by the method of prior art (3) for independently evaluating the phases of individual measured data pieces when measurement of prior art (2) is carried out.
In the method of independently evaluating The phases of the individual measure data pieces, there needs the processing of eliminating offset due to non-uniformity of static magnetic field and therefore, a phase presumptive image 310 for the static magnetic field non-uniformity is prepared by means of an image filter 300 for low-pass filtering so as to correct the static magnetic field non-uniformity.
Measured images formed by reconstructing the individual measured signals are four kinds of images 101 to 104, and causes for assignment of phases are indicated in parenthesis in order of static magnetic field non-uniformity, x-direction flow velocity sensitivity measurement, y-direction flow velocity sensitivity measurement and z-direction flow velocity sensitivity measurement.
For example, (+, -, +, +) shows that phase assignment due to static magnetic field inhomogeneity is +.theta.h, phase assignment due to x-direction flow velocity is -.theta.x, phase assignment due to y-direction flow velocity is +.theta.y and phase assignment due to z-direction flow velocity is +.theta.z.
The phase assignment due to static magnetic field inhomogeneity .theta.h has different values for different sites and has the same value for individual measurement cycles. The phase assignment .theta.x has a value proportional to x-direction flow velocity and its sign is determined by the manner of applying the flow encode pulses in the individual measurement cycles. Signs of .theta.y and .theta.z are similarly determined by the manner of applying the flow encode pulses in the individual measurement cycles.
The respective measured images 101 to 104 are vector images each of which has vectors having the magnitudes and directions at respective points on an image. The phase is an angle a vector makes to a predetermined axis direction so as to represent a direction of the vector.
One measured image 101 is subjected to the processing of low-pass filtering by means of the image filter 300 to form a phase presumptive image 310 for static magnetic field inhomogeneity. Roughly speaking, the phase presumptive image is a vector image roughly capturing static magnetic field distortion.
Next, an arithmetic operation for subtraction of phase by a phase of the phase presumptive image 310 is applied to each of the images to form corrected images 301 to 304 subject to phase correction. The corrected images 301 to 304 are vector images which are almost removed of the phase assignment due to static magnetic field and an uncorrected remaining phase assignment is indicated by d in the Figure.
Next, the phases of the individual corrected images 301 to 304 are evaluated to form phase images 311 to 314. When a flow velocity image in The x direction is desired to be prepared, the phase images 311 and 312 are added along with addition of the phase images 313 and 314 and a difference between both the sums is calculated and multiplied by a predetermined coefficient to determine a flow velocity in the x direction. Similarly, flow velocity images in the y and z directions can be obtained and images indicative of the magnitudes of flow velocities can be obtained.
However, in the above method of FIG. 3, there arise problems that much time is consumed for arithmetic operation of phase correction using the image filter 300 for low-pass filtering and in addition, even the phase images subject to the phase correction have phases which depend on three flow velocities in the x, y and z directions and eventually the aliasing error is increased by evaluating the phase directly from one image.